Answer:
Jack's final bank account amount will be $54,782.50, earning $7,459.31 in interest.
General Formulas and Concepts:
Algebra I
Compounded Interest Rate Formula: [tex]\displaystyle A = P \bigg( 1 + \frac{r}{n} \bigg) ^{nt}[/tex]
A is final amountP is principle amountr is raten is compounded ratet is timeStep-by-step explanation:
Step 1: Define
Identify given variables.
P = $47,323.15
r = 0.05
n = 1
t = 3
Step 2: Find Interest
[Compounded Interest Rate Formula] Substitute in variables:∴ Jack will gain $7,459.31 and have a net balance of $54,782.50.
---
Learn more about Algebra I: https://brainly.com/question/27710663
---
Topic: Algebra I
marking brainliest if correct
four numbers that are evenly divisible by both 4 and 9.
four numbers that are evenly divisible by 2, 3, and 5.
Answer:
36, 72, 108, 144
30, 60, 90, 120
Step-by-step explanation:
i need an equation with a variable on each side that equals 15
Answer:
2x + 5 = 3x
Step-by-step explanation:
In this equation, x = 5 and both sides equate to 15. Hope this helped!
Represent geometrically the following numbers on the number line: √4.5 √8.3. (step by step explanation preferably done in notebook please) I’ll mark the best answer as brainliest
Answer:
To represent geometrically √x on a number line:
Draw a line segment AB with length x (where point A is -x and point B is zero on the number line).Extend AB by drawing a line segment BC of length 1 unit.Draw a line perpendicular to AC at point B.Let O be the midpoint of AC.To represent geometrically √4.5 on a number line:
Draw:
Point A = -4.5Point B = 0Point C = 1Draw a line perpendicular to AC at point B.
Let O be the midpoint of AC:
[tex]\implies \sf O=\dfrac{-4.5+1}{2}=-1.75[/tex]
Draw a semicircle with center O and radius OA
[tex]\implies \sf OA=\dfrac{AC}{2}=\dfrac{5.5}{2}=2.75[/tex]
Let point D be where the semicircle intersects with the perpendicular line
[tex]\implies \sf BD=\sqrt{AB}=\sqrt{4.5}[/tex]
Draw an arc with center B and radius BD from point D to the number line.
[tex]\implies \sf BE=\sqrt{4.5}[/tex]
⇒ Point E is [tex]\sf \sqrt{4.5}[/tex] on the number line.
Attachment 2To represent geometrically √8.3 on a number line:
Draw:
Point A = -8.3Point B = 0Point C = 1Draw a line perpendicular to AC at point B.
Let O be the midpoint of AC:
[tex]\implies \sf O=\dfrac{-8.3+1}{2}=-3.65[/tex]
Draw a semicircle with center O and radius OA
[tex]\implies \sf OA=\dfrac{AC}{2}=\dfrac{9.3}{2}=4.65[/tex]
Let point D be where the semicircle intersects with the perpendicular line
[tex]\implies \sf BD=\sqrt{AB}=\sqrt{8.3}[/tex]
Draw an arc with center B and radius BD from point D to the number line.
[tex]\implies \sf BE=\sqrt{8.3}[/tex]
⇒ Point E is [tex]\sf \sqrt{8.3}[/tex] on the number line.
x ^ 2 + y ^ 2 + 6y - 67 = 2y - 6x; circumference
Answer:
(x+3)^2+(y+2)^2=80
Step-by-step explanation:
A garden has the shape of a circular sector such that its straight sides measure 50 feet in length and the central angle is 132°. if the garden needs to be surrounded by fencing, how many feet are needed to enclose the garden?
Answer:
215 ft
Step-by-step explanation:
The length of the surrounding fence is equal to the perimeter of the garden. That is the sum of the lengths of the straight sides and the curved arc. The arc length is given by the formula ...
s = r·θ . . . . . where θ is the central angle in radians
__
arc lengthThere are π radians in 180°, so the arc will have a measure in radians of ...
θ = 132° × (π/180°) = 11/15π ≈ 2.3038 . . . . radians
Then the length of the curved side of the garden is ...
s = (50 ft)(2.3038 radian) ≈ 115.2 ft
__
perimeterThe fence length is the sum of the arc length and the two radii:
perimeter = 115.2 ft + 2×50 ft = 215.2 ft
About 215 feet of fencing are needed to enclose the garden.
Write 12x + 4y= –36 in slope-intercept form. y= x− .
[tex]~~~~~12x+4y = -36\\\\\implies 3x +y = -9\\\\\implies y = -3x -9[/tex]
- - - - - - - - - - - - - - - - - - - -- - - - - - - - - - -- - - - - - -- - - - - - - - --
[tex]\blue\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]
Write 12x+4y=-36 in slope intercept form.
[tex]\blue\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}[/tex]
Slope intercept form looks like so:-
y=mx+b
Right now the line's equation is written in standard form, ax+by=c.
First, subtract 12x on both sides:-
4y=-36-12x
Now divide by 4 on both sides:-
y=-9-3x
On further simplification,
switch -9 and -3x places (it's not mandatory)
y=-3x-9
That's our equation in slope intercept form.
Good luck.- - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - -- - - -
In the figure, ∆ABD ≅ ∆CBD by Angle-Side-Angle (ASA). Which segments are congruent by CPCTC?
Answer: AB ≅ CB
Step-by-step explanation:
In the given figure, we have ∆ABD ≅ ∆CBD
The CPCTC property of congruent triangles says that if two triangles are congruent then their corresponding parts ( angles and segments ) are congruent.
Since we have given that ∆ABD ≅ ∆CBD.
Therefore, the corresponding segments are congruent.
As segment AB is corresponding to segment CB. [First two letters]
Therefore, segment AB is congruent to segment CB.
PLEASE HELP IM GIVING 15 POINTS !!!!! how would you solve y=x^2+4x-1 ? and how would you solve y-7x=9 ?
Graph the equation. y = 4(x + 6)(x + 4)
There you go I hope its correct
??? ??????????????????????
Answer:
28.86338
Step-by-step explanation:
find the area of the whole circle and then divide by 3, since the shaded part is about 1/3 of the whole cricle.
Which equation represents the distance d traveled in t hours?
Answer:
d is the right answer hope this helps
What is the area of the shape shown below? Round your answer to the neatest tenths
Answer:
42.5
Step-by-step explanation:
Area- (9.0×3.5) +1/2(5×2) + (2×2)
=31.5+2+5+4
=42.5
hope it helps!!!
Solve the inequality.
2(4x
3) 2 -3(3x) + 5x?
O x 2 0.5
X 2 2
(-09 0.5]
(-c0, 2]
Answer:
Use the given functions to set up and simplify (-c⁰, 2]
Step-by-step explanation:
2(4x ⋅ 3) = 24x
2-3 (3x) + 5x = -4x + 2
Ox ⋅ 2 = 2Ox
0.5 = 2Ox
X ⋅ 2 = 2X
2 = 2X
-9 ⋅ 0.5 = -4.5
(-c⁰, 2] = (-1,2]If this was helpful, let me know!
Warm up: solve for the variable
3 = x/5
Answer:
x=15
Step-by-step explanation:
multiply 5 by both sides to get rid of 5 on the second side --> 3x5=x/5x5
15=x
ur wecome :)
brainliest please?
John is traveling at 48 miles per hour and his distance can be written as d = 48t.
How far will John travel if he travels for 5 hours?
Answer:
240 miles
Step-by-step explanation:
To find how far John will travel is he travels 48 miles per hour for 5 hours, you can multiply John's speed (48 mph) with his travel time (5 hours) to get:
48 mph × 5 hours = ?
48 × 5 = 240
Therefore, John will travel 240 miles if he travels for 5 hours at 48 miles per hour.
welp pls.i’m so confused
Answer:
Length = 17 units
Width = 1 unit
Step-by-step explanation:
[tex]A = l * b[/tex]
[tex]17 = (2x+1) (x-7)\\17 = 2x^{2} -14x+x-7\\17 = 2x^{2} -13x-7\\2x^{2} -13x-7-17=0\\2x^{2} - 13x -24=0\\(2x+3) (x-8)=0\\x=-\frac{3}{2} or x=8\\[/tex]
but x cannot be negative because length and width cannot be negative;
[tex]x\neq -\frac{3}{2} : x = 8[/tex]
Length:-
[tex]=2x +1\\=2(8)+1\\=17units[/tex]
Width:-
[tex]=x-7\\=8-7\\=1 unit[/tex]
Write a sine function that has an amplitude of 5, a midline of 2 and a period of 3/7
A sine wave is also known as a sinusoid. The sine function that has an amplitude of 5, a midline of 2 and a period of 3/7 is 5Sin(16πx/3)+2.
What is sine function?A sine wave, also known as a sinusoid, is the graph of the sine function. Any curve that can be expressed in the form is referred to as a sinusoid. (A and B are both positive.) Sinusoids are the most generic version of the sine function.
Given the amplitude of the function is 5, the vertical shift is 3, and the period of 3/7. Therefore, the values of constants can be written as,
a = 5
b = (2π)/(3/7) = 14π/3
d = 2
Substituting the values in the sine function,
a sin b (x-c) + d
= 5 Sin(16π/3)(x-0) + 2
= 5 Sin(16πx/3) + 2
Hence, the sine function that has an amplitude of 5, a midline of 2 and a period of 3/7 is 5Sin(16πx/3)+2.
Learn more about Sine function:
https://brainly.com/question/12015707
#SPJ1
Find the value of x.
148°
Гу
х
x = [? ]°
=
The sum of two numbers is 24. Twice the first number plus the second is 26. Find the numbers.
Answer:
2 and 22
Step-by-step explanation:
You can put them into equations:
x+y=24 and 2x+y=26
Then, for each equation solve for one of the variables. It doesn't really matter which one but I chose y here.
y=24-x and y=26-2x
Since both equations are equal to y it means that the expression on the right sides of the equal sign are equal to each other:
24-x=26-2x
From here solve for x and you are left with:
x=2
Now that you know one variable go back and plug it into an equation and solve for y. Again, it doesn't matter which one you choose, you will end up with the same answer:
(2)+y=24
So..
y=22
Given: x - 8 > -3. solution set
Answer: x > 5
Reason:
Add 8 to both sides to undo the -8
We have x-8 > -3 become x > -3+8 which becomes x > 5
We can replace x with anything larger than 5.
To graph this on a number line, plot an open hole at 5. Then shade to the right.
Find the area of the parallelogram. Round to the nearest hundredth if necessary.
6 m
8 m
Area =
cm2
Answer:
48 square cm.
Step-by-step explanation:
The area of a parallelogram is (A = B * H)
Base is 8
Height is 6
8*6 = 48 square cm.
What is the slope of the line that passes through the points (-4,-7) and
(-2,-19)? Write your answer in simplest form.
For what values of b is the relation R:{(b^2, 5), (5b, 6)} NOT a function?
Answer:
b=0,b=5
Step-by-step explanation:
A rectangular prism fish tank measures 6.2 cm × 4.7 cm × 2.3 cm.
Find the volume of the fish tank and round to the nearest hundredth if necessary.
Answer:
The volume of the fish tank is 67.02
Step-by-step explanation:
To find the volume of a rectangular prism, multiply length times width times height.
V = L*W*H
V = 6.2*4.7*2.3
V = 67.022
67.022 rounded to the nearest hundredth would equal 67. 02
The attached image shows a few of the different volume formulas.
H. e. l. p
____
( - ^ • )
( > > )
MeEee
For the part 1 volume is 32.768 dm³, for part 2 side length is 6 meters, and for part 3 the volume is 480 cubic cm.
What is a cube?It is defined as three-dimensional geometry that has six square faces and eight vertices.
We have
1) Side length = 3.2 dm
Volume = (3.2)³ = 32.768 dm³
2) Volume of cube = 216 cubic meters
a³ = 216
a = 6 meters
3) The dimensions for sewing box: 10 cm, 8 cm, and 6 cm
Volume = 10×8×6 = 480 cubic cm
Similarly, we can calculate the rest of the data.
Thus, for the part 1 volume is 32.768 dm³, for part 2 side length is 6 meters, and for part 3 the volume is 480 cubic cm.
Learn more about the cube here:
brainly.com/question/15420947
#SPJ1
if you borrow 800$ for 10 years and the interest rate is 7% how much do you pay altogether?
Answer:
Answer is
1,760
Step-by-step explanation:
960+800=1,760
Two metal disks, one with radius r = 2. 50 cm and the other with radius r = 5. 00 cm are welded together and
The total moment of inertia of the two disks will be I = 2.375 × 10-³ Kgm² welded together to form one unit.
What is moment of inertia?Moment of inertia is the quantity expressing a body's tendency to resist angular acceleration, which is the sum of the products of the mass of each particle in the body with the square of its distance from the axis of rotation.
Using the formulas to calculate the moment of inertia of a solid cylinder:
I = ½MR²
Where;
I = moment (kgm²)
M = mass of object (Kg)
R = radius of object (m)
Total moment of inertia of the two disks is expressed as: I = I(1) + I(2)
That is;
I = ½M1R1 + ½M2R2
According to the provided information;
R1 = 2.50cm = 0.025m
M1 = 0.800kg
R2 = 5.00cm = 0.05m
M2 = 1.70kg
I = (½ × 0.800 × 0.025²) + (½ × 0.05² × 1.70)
I = (½ × 0.0005) + (½ × 0.00425)
I = (0.00025) + (0.002125)
I = 0.002375
I = 2.375 × 10-³ Kgm²
Hence The total moment of inertia of the two disks will be I = 2.375 × 10-³ Kgm² welded together to form one unit.
To know more about moment of inertia follow
https://brainly.com/question/14460640
#SPJ4
Please help me find the mean and the median:
Answer:
anyways your answer is 1
Step-by-step explanation:
The circumference of the earth is 2.4x109 miles. if you traveled at an average of 8.5x10 miles per hour, how long would it take for you to go around the earth? round your answer to the nearest whole number.
a. 2,820 hours
c. 354 hours
b. 282 hours
d. 3,500 hours
Answer:
282 hr <======= see below
Step-by-step explanation:
Distance / rate = time
2.4 x 10^9 mi / 85 m/hr = 28235294 hr
You must have left the power of 10 off of your speed
probably should be 8.5 x 10^6 perhaps? then answer is 282
If speed was 8.5 x 10^5 then answer becomes ~ 2820
Javior has an equal number of dimes, nickels and
quarters. He has a total of $2.40. How many coins
does he have all together?
?
Dimes:
Nickels:
Quarters:
?
?
Answer:
?